We present the results of a deep HST/WFPC2 imaging study of 17 quasars at z~=0.4, designed to determine the properties of their host galaxies. The sample consists of quasars with absolute magnitudes in the range −24 ≥ MV ≥ −28, allowing us to investigate host galaxy properties across a decade in quasar luminosity, but at a single redshift. Our previous imaging studies of AGN hosts have focussed primarily on quasars of moderate luminosity, but the most powerful objects in the current sample have powers comparable to the most luminous quasars found at high redshifts. We find that the host galaxies of all the radio-loud quasars, and all the radio-
quiet quasars in our sample with nuclear luminosities MV < −24, are massive bulge-
dominated galaxies, confirming and extending the trends deduced from our previous
studies. From the best-fitting model host galaxies we have estimated spheroid and
hence black-hole masses, and the efficiency (with respect to the Eddington luminosity)
with which each quasar is emitting radiation. The largest inferred black-hole mass in
our sample is MBH~=3×10^9M⊙, comparable to the mass of the black-holes at the centres of M87 and Cygnus A. We find no evidence for super-Eddington accretion rates in even the most luminous objects (0.05 < L/LEdd < 1.0).
We investigate the role of scatter in the black-hole:spheroid mass relation in determining the ratio of quasar to host-galaxy luminosity, by generating simulated populations of quasars lying in hosts with a Schechter mass function. Within the subsample of the highest-luminosity quasars, the observed variation in nuclear-host luminosity ratio is consistent with being the result of the scatter in the black-hole:spheroid relation. Quasars with high nuclear-host luminosity ratios can be explained in terms of sub-Eddington accretion rates onto black-holes in the high-mass tail of the black-hole:spheroid relation. Our results imply that, owing to the Schechter function cutoff, host mass should not continue to increase linearly with quasar luminosity, at the very highest luminosities. Any quasars more luminous than MV=−27 should be found in
massive elliptical hosts which at the present day would have MV~=−24.5 (Refer to PDF file for exact formulas).

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Based on observations with the NASA/ESA Hubble Space Telescope, (program ID’s 7447 and 8609) obtained at the Space Telescope Science Institute, which is operated by The Association of Universities for Research in Astronomy, Inc. under NASA contract No. NAS5-26555. This research has made use of the NASA/IPAC Extragalactic Database
(NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. James Dunlop acknowledges the enhanced research time afforded by the award of a PPARC Senior Fellowship. DJEF, MJK, RJM & WJP also acknowledge PPARC funding. We thank the anoymous referee for a fair and constructive
critique which has led to significant improvements in this paper.